### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014

### Keywords

Chromatic number Almost countably chromatic Large Cardinals stationary hitting specializable Souslin tree Almost-disjoint famiy tensor product graph Small forcing ccc Hereditarily Lindelöf space Chang's conjecture Ostaszewski square S-Space Antichain Fat stationary set Rainbow sets Hindman's Theorem reflection principles Square-Brackets Partition Relations PFA(S)[S] xbox Parameterized proxy principle OCA Rado's conjecture Singular coﬁnality Erdos Cardinal Distributive tree 11P99 Martin's Axiom Erdos-Hajnal graphs Prevalent singular cardinals Kurepa Hypothesis Singular cardinals combinatorics Nonspecial tree Non-saturation very good scale Diamond square principles Foundations Constructible Universe PFA middle diamond Partition Relations 05A17 Uniformization Jonsson cardinal Hedetniemi's conjecture Microscopic Approach Successor of Singular Cardinal Absoluteness sap super-Souslin tree Luzin set Souslin Tree b-scale Uniformly coherent Ascent Path Sakurai's Bell inequality coloring number stationary reflection Shelah's Strong Hypothesis Postprocessing function Stevo Todorcevic Singular Density Prikry-type forcing Cardinal function Dushnik-Miller Successor of Regular Cardinal diamond star Almost Souslin Knaster Cohen real Coherent tree Fodor-type reflection HOD Aronszajn tree P-Ideal Dichotomy Rock n' Roll Slim tree Fast club weak diamond Universal Sequences Reduced Power Selective Ultrafilter L-space Generalized Clubs Forcing Axioms Weakly compact cardinal projective Boolean algebra Forcing Club Guessing Poset incompactness Commutative cancellative semigroups polarized partition relation approachability ideal Cardinal Invariants free Boolean algebra Whitehead Problem square Mandelbrot set Minimal Walks Axiom R weak square free Souslin tree

# Tag Archives: 03E50

## Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading